JP3516232B2 - Method and apparatus for implementing feedback control that optimally and automatically rejects disturbances - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a controller used for process control, and more specifically, a control capable of estimating a state of a control target and an unknown disturbance based on an input signal and an output signal of the control target. Regarding vessels.

[0002]

2. Description of the Related Art Controllers used in modern process control are mainly PID (Proporti) developed around the 1940s.
onal ・ Integral ・ Derivative: Proportional / integral / derivative) regulator and its variants. In the 1960s, the modern control theory based on the mathematical model of the controlled object made great progress. However, in actual control, it was difficult to extract an appropriate mathematical model of the controlled object.
Therefore, it is difficult to apply the modern control theory to an actual controlled object without an appropriate mathematical model. So, from the 1980s, many "new control" methods-
The "advanced control method" has emerged. However,
In the end, these "advanced control methods" also failed to break away from the constraints of mathematical models. In other words, since complicated processes such as "model creation", "system recognition", and "adaptation" were adopted, the control algorithm became complicated, which became a major limitation in actual application.

PID control, which was born in the early stages of control theory and analog technology, has been used as one completed control technology at the time in many actual control sites because it successfully achieved the goal of each control. . However, due to the rapid development of science and technology, the control targets are diversified, and the demands for control accuracy and control speed are increasing, and primitive PID control can no longer respond to the complicated changes of the new era. It was going on. Therefore, considering that it is the greatest drawback of PID control that the controlled object cannot be precisely described by mathematics, there has been a movement to seek a control technique for expressing the controlled object by a new expression method. Therefore, 1
Since the 960s, modern control theory based on an accurate mathematical model (state space model) of a controlled object has made great progress. However, this new theory failed to provide guidance on how to design a practical controller. Therefore, the result was difficult for actual application. Then, from the end of the 1980s, a new boom occurred, "Let's recognize PID control again."

From these circumstances, in order to find a practical and efficient controller, it is essential to identify the advantages and disadvantages of PID control and modern control theory. The main reason why PID control is often applied in process control is not to determine the control operation based on the mathematical model of the controlled object, but to find the “error between the target value and the actual amount of behavior of the controlled object”. The point is that the control operation of eliminating the error is adopted. However, when the operation amount for the controlled object is obtained by this method, due to the limitations such as the recognition level and technical conditions at that time,
Direct processing of "error between target and behavior" by a relatively "simple process" combining past (I), present (P), and change tendency (D) of "error between target value and behavior amount" By doing so, the manipulated variable was determined. The limit of PID control was actually "simple processing" of such "target signal" and "actual behavior signal". In short, the "model-independent" aspect was an advantage, but the "simple process" was its drawback. On the other hand, modern control theory has made a great contribution in the analysis of systems (that is, the method of analyzing the system of controlled objects), but in actual control, it is not possible to determine an appropriate mathematical model for many controlled objects. However, it was difficult to actually apply the above control method. In other words, the "model-dependent" aspect is an advantage of modern control, but the "practical use" aspect is a drawback.

If we combine the system analysis technology based on the modern control theory for the controlled object with the modern signal processing technology, and inherit the "model-independent" advantage of the PID control, the "simple processing" method. If it can be improved, a new type practical controller with better performance than the conventional PID control can be made.

[0006]

The above-mentioned conventional PID technique has the following four problems to be improved. The target value may change rapidly, but the actual behavior of the controlled object changes gradually due to inertia. It is not appropriate to make such an actual behavior follow a rapidly changing target value. There is a lack of proper method to obtain the derivative signal of the error. “Past” (ie I (integration)), “present” regarding error
(Ie P (proportional action)), and “change trend” (ie D
The (differential) combination is not necessarily the best combination. The introduction of I (integral) plays a certain role in eliminating the influence of an unknown steady value, that is, disturbance, but it has little meaning other than that. Prior to the present invention, the inventor of the present application invented the following control technique capable of solving the above-mentioned four problems relating to PID control. The inventor has invented a technique of setting an appropriate “transient process” and a differential signal of this process in advance based on the target value and the attribute of the controlled object. A nonlinear dynamic system "Nonlinear tracking differentiator" (Tracking-Differentia) that can extract differential signals rationally
tor: TD) was invented. For more information on this technology,
It is disclosed in the following document A and Chinese documents [1] and [2] of Table 1. Reference A: Han Jing-Qing. Nonliner Design Methods For
Control Systems.IFAC World Congress 1999, Beijin
g, PRChina, C-2a-15-4, 521-526, (5th-9th July 199
9). (Note: IFAC: The International Federation of Auto
matic Control) A technique has been invented that calculates an operation amount for a controlled object by an appropriate nonlinear algorithm based on an error between a set transient process and an actual state of the system. Details of this technique are disclosed in Chinese literature [3] of Table 1. A non-linear dynamic system "Extended State Observer" (Extended State Observer) that can extract the state of the controlled object and the unknown disturbance based on the input signal and output signal of the controlled object
er: ESO) was invented. Details of this technique are disclosed in the above-mentioned document A, the following document B, and Chinese document [4] in Table 1. Reference B: Bags Mahawan, Luo Sanghua, Han Kyosei (inventor of the present application), Shinichi Nakajima: "High-speed and high-precision motion control of robots by extended state observer", Journal of the Robotics Society of Japan, Vol. 18, No. 2, pp. 244-251
2000 This "extended state observer" is an independent entity regardless of the specific mathematical model of the controlled object.

The inventor of the present application invented a new type of non-linear PID controller based on the above four techniques. In this controller, first, the first "tracking differentiator" sets the transient process and extracts its differential signal. The second "tracking differentiator" then follows the actual behavior of the controlled object and extracts its differential signal. Then, the error between the transient process set by the first "tracking differentiator" and the actual behavior followed by the second "tracking differentiator", the differential signal of the transient process and the actual behavior The differential error from the differential signal is calculated. Further, the above error is integrated. Finally, the manipulated variable for the controlled object is generated by non-linearly combining the integrated output and the error and the differential error. For details of this technique, see FIG.
1 and the Chinese document [4] of Table 1. The above-mentioned new-type nonlinear PID controller is superior to the conventional PID controller in its control effect, strong against external disturbance, and easy in parameter adjustment.

Subsequently, the inventor of the present application applies the idea of the state observer and the special effects of nonlinear feedback to enhance the ability of the controller to adapt to the uncertainties and the ability to cope with unknown disturbances. We have developed an "extended state observer" that is strong in estimating the state, uncertainties and disturbance of the controlled object based on the input and output signals of the controlled object. (Auto-Disturbances-Rejectio
n Controller: ADRC) was invented. Since the "extended state observer" was also able to estimate uncertain disturbances, in ADRC the feedback of the first error integral mentioned above was no longer necessary. Details of this technique are disclosed in Section 4.2 (Fig. 2) of Document A and Chinese documents [5] and [6] of Table 1.

The ADRC is composed of the following three parts. The first part is the "tracking differentiator (TD)"
Sets the transient process and extracts its derivative signal. The second part is "Extended State Observer (ESO)"
Estimates the state variable of the controlled object and the actual effect of the unknown disturbance. Then, as a third part, the transient process set by the "tracking differentiator" and the state variable of the controlled object estimated by the "extended state observer" are nonlinearly combined, and the disturbance estimated by the "extended state observer" is further added. The operation amount for the controlled object is generated by compensating the action amount of.

All three parts of the ADRC above use appropriate non-linear characteristics. This is not difficult for a digital controller. In other words, the digital controller cannot make a distinction between linear and non-linear, but simply executes the program of the given nonlinear algorithm.

ADRC is perfectly adapted to the demands of the digital control age. Moreover, it is difficult to realize the conventional PID controller, system control of a large time delay control target model, decoupling control for a multivariate system (because ESO can estimate all uncertain effects in an integrated manner), etc. Is now relatively easy to do. A
The DRC was able to completely unify deterministic system control and uncertain system control.

However, from the viewpoint of practicality, the automatic disturbance rejection controller has a problem to be further improved. The problems to be improved from the “automatic disturbance rejection controller (ADRC)” are the following three points. When the "tracking differentiator (TD)" sets a transient process, since the acceleration changes abruptly, the manipulated variable of the transient process tends to change abruptly. At times, it can cause difficulties in the actual control process. The amount of calculation of the nonlinear function in the "extended state observer (ESO)" is relatively large. The nonlinear feedback form of error and differential error needs to be optimized.

The present invention provides an "automatic disturbance rejection controller (ADR).
C) ”is to improve the above three problems.

[0014]

[Table 1]

[0015]

[0016]

[0017]

[0018]

The first aspect of the present invention is as follows.
It includes an operation to convert the error between the estimated displacement of the controlled object state and the actual displacement of the controlled object state using a conversion function that can include a non-linear function. We assume an extended state observation method using an observer that can observe uncertain effects including the dynamic characteristics of and through state variables.

First, an operation for converting an error using a conversion function is executed as an operation for converting an error using a polygonal line function. More specifically, the polygonal line function is defined as the expression 1 of claim 1. Then, based on the output value of the calculation, the estimated value of each state of the controlled object and the estimated value of the uncertain effect are calculated using the observer.

A second aspect of the present invention is a displacement error which is an error between the displacement of the estimated value of the controlled object state and the displacement of the transient process of the target value, and the derivative of the displacement of the estimated value of the controlled object state. A transformation that can include a non-linear function that calculates a displacement differential error, which is an error between the target value and the differential of the displacement of the transient process, and inputs the displacement error and the displacement differential error, and converges both of these errors to zero. It is premised on a feedback control method for compensating the displacement of the state of the controlled object by calculating a function, calculating an error feedback manipulated variable which is an operated amount for the controlled object, and controlling the controlled object.

Then, as the conversion function, when the displacement error and the displacement differential error are converged to zero, a function having a characteristic of suppressing the occurrence of vibration near the zero of those error values is set. More specifically, the conversion function is calculated based on the formula 2 of claim 2.

[0022]

[0023]

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Configuration of an Embodiment of the Present Invention FIG. 1 is a configuration diagram of an optimum automatic disturbance rejection controller (optimum ADRC) 101 realized as an embodiment of the present invention.

The optimum ADRC 101 is composed of the following functional parts. First, the transient process setter (ATP: Ar
range of Transient Process) 102 is the target value v
Generate a transient process displacement v1 and a transient process displacement derivative v2 with respect to 0.

Extended State Observer (ESO: Extended State)
Observer) 103 estimates the state of the controlled object and the uncertain disturbance action, and uses the estimated state displacement z1 and the estimated state displacement derivative z2, which are the estimated values of the controlled state, and all uncertain models and uncertain disturbances. An uncertain effect estimated value z3 that is an estimated value of the action is output. The input to the ESO 103 is the value bu obtained by multiplying the manipulated variable u for the controlled object by the known coefficient b in the multiplier 104 and the known action amount calculator 10
5 is a value obtained by adding the known action amount f0 output by 5 with the adder 106, and the output value y of the controlled object.

The error calculator 107 uses the A.D. T. P 102
The displacement error ε1 which is the error between the transient process displacement v1 generated by the above and the state estimation value displacement z1 of the controlled object output by the ESO 103 is calculated. The differential error calculator 108 uses the A.D.
T. Displacement differential error ε2, which is an error between the transient process displacement differential v2 generated by P 102 and the state estimation value displacement differential z2 of the controlled object output by the ESO 103, is calculated.

Optimal state error feedback device (O.S.
E. F) 109 outputs an error feedback manipulated variable u00 that optimally compensates for these errors based on the displacement error ε1 and the displacement differential error ε2. On the other hand, ESO 103
Uncertainty effect estimated value z3 and known effect quantity calculator 1
The value obtained by adding the known action amount f0 output from the adder 05 by the adder 110 and the value obtained by multiplying the known coefficient −1 / b by the multiplier 111 are added to the adder 112 as the disturbance compensation operation amount u1. Entered in.

The adder 112 is an O.D. S. E. F 109
Error feedback manipulated variable u00 and multiplier 11
The value obtained by adding the disturbance compensation manipulated variable u1 output by 1 is output as the manipulated variable u for the controlled object. In the above configuration, the known effect amount computing unit 105 uses the ESO 1
A known function amount f0 is obtained by executing a known function operation f0 (z1, z2, w0) based on the estimated state value displacement z1 and the estimated state value displacement derivative z2 output by 03 and the known disturbance action amount w0. To calculate. The known effect amount calculator 105 is not essential and may be omitted if the known effect amount is unknown.

Further, as a feature particularly related to the present invention,
The transient process pattern selection unit 113 uses the A. T. P 1
02 is a function of the transient process pattern used in generating the transient process displacement v1 and the transient process displacement derivative v2 with respect to the target value v0, based on the user's instruction,
Select from multiple patterns stored in advance,
A. T. Supply to P 102.

Similarly, as a feature particularly related to the present invention,
The non-linear function selection unit 114 uses the non-linear functions g1 and g to be used when the ESO 103 calculates the state estimated value displacement z1, the state estimated value displacement derivative z2, and the uncertain effect estimated value z3.
2 and g3 are selected from a plurality of types stored in advance based on a user's instruction and supplied to the ESO 103.

Further, as a feature particularly related to the present invention,
Although not shown in particular, S. E. F 109 uses an optimized non-linear function to calculate the error feedback manipulated variable u00. Description of Operation of Embodiment of Present Invention The operation of the embodiment of the present invention having the above-described configuration will be described below. <A. T. Operating Principle of P 102> As described as the problem of “Problems to be solved by the invention”, it is not appropriate to make the actual behavior of the controlled object that gradually changes due to inertia follow the rapidly changing target value. Absent. Therefore,
A. T. The P 102 does not directly use the target value v 0 when performing feedback control for the controlled object, but generates a transient process displacement v 1 and a transient process displacement derivative v 2 with respect to the target value v 0, and uses it for the controlled object. Used for feedback control.

The setting of the transient process is determined by the target value v ₀ and the transient process time T of the controlled object. First, the interval [0 T] of the transient process is [0 T ₁ ] and [T ₁
T]. The first half is the acceleration stage,
The second half is the deceleration stage. 1. That is, 0 ≦ t ≦ T ₁
In setting the a (t)> 0, T 1 ≦ t ≦ T with a (t) <0, t > T 1 in such that a (t) = 0, the acceleration a (t).

[0033]

[0034]

(2) The integral of a (t) on the interval [0 T] is 0. That is, the area of the plus region and that of the minus region of a (t) are the same. The transient process displacement derivative v2 can be obtained by integrating the acceleration a (t) from 2.0 to t (0≤t≤T). That is, the speed of the transient process can be acquired. 3. The transient process displacement v1 can then be obtained by integrating the transient process displacement derivative v2 from 0 to t. 4. To simplify the algorithm, the acceleration a (t) has a polynomial form. Based on the above condition settings 1 to 4, the inventor of the present application defines “τ = t / T”, and then the following formula 3 and FIG. 2, formula 4 and FIG. And the acceleration of the transient process a shown as FIG. 4 and Eq. 6 and FIG. 5, respectively.
A set of (t), transient process displacement v1, and transient process displacement derivative v2 was determined.

[0036]

[Equation 3]

[0037]

[Equation 4]

[0038]

[Equation 5]

[0039]

[Equation 6]

Equation 3 and FIG. 2 are transient process characteristics corresponding to a control target pattern having a rapid change in acceleration at the start and end of the transient process. Formula 4 and FIG. 3 are transient process characteristics corresponding to the control target pattern in which the acceleration changes at the end of the transient process.
Formula 5 and FIG. 4 are transient process characteristics corresponding to the control target pattern in which the acceleration changes at the time of startup. Formula 6 and FIG. 5 are transient process characteristics corresponding to the control target pattern in which the acceleration does not change at the time of starting and ending. In the embodiment of the present invention, when the user sets a transient process in the controlled object, the user sets the transient process pattern selection unit 11 in FIG. 1 according to each feature in the input of the controlled object.
3, by designating one of the four transient process patterns shown in the above equations 3 to 6,
The desired arithmetic expressions regarding the transient process displacement v1 and the transient process displacement derivative v2 are described in A. T. It can be set to P 102. The calculation formula for the acceleration a (t) is not used. <Operation Principle of ESO 103> The ESO 103 can estimate the state of the controlled object and the unknown disturbance.

First, the state variable of the controlled system is x,
Let us assume that the input is u and the output is y, and consider the following 1-input / output quadratic nonlinear system.

[0042]

[Equation 7]

Where w0 is a known bounded disturbance, w is an unknown bounded disturbance, f0 (x, dx / dt, w0) is a known dynamic characteristic of the system including the known disturbance, and f1 ( x, d
x / dt, w) (hereinafter referred to as f1 (.) for simplicity) is an unknown dynamic characteristic of the system including an unknown disturbance. It is assumed that f1 (.) is not known exactly or cannot be measured accurately. Note that f0 (x, dx / dt, w
0) need not be included if unknown. b is input u
Is a gain, and its value is known. In the formula 7, two can be measured, x and u. ESO 1
The most important function of 03 is unknown dynamic characteristic f1
(•) is to be estimated. If an observer that estimates f1 (.) can be designed, the unknown dynamic characteristic f1 (.) can be compensated by feeding back the estimated value to the manipulated variable u (FIG. 1) of the controlled object.

For that purpose, first, the following variables are defined.

[0045]

[Equation 8]

From the above equation 8, the first line of the equation 7 is transformed into the following equation.

[0047]

[Equation 9]

The above equation (9) is a model for constructing the ESO 103. What is important here is that the dynamic characteristic f1 (.) Of the controlled system is simply a function of time a (a (t)
). Note that this a is independent of the acceleration a or a (t) in the equations 2 to 6,
A variable used only inside an expression.

Next, a new state variable represented by the following equation is defined.

[0050]

[Equation 10]

From Equation 10, the nonlinear system of Equation 9 can be rewritten as the following equation of state.

[0052]

[Equation 11]

X3 in the above equation 11 is called an "extended state variable". In order to estimate the state variables x1, x2, x3, a non-linear observer represented by the following equation is constructed. This theory is disclosed in the Chinese document [4] in Table 1 above.

[0054]

[Equation 12]

Β01, β02 included in the above equation 12
β03 (> 0) is a constant called adaptive gain. Further, g1 (ε), g2 (ε) and g3 (ε) are non-linear functions appropriately determined by the user regarding the error ε. z1 and z2 are the displacement of the estimated value of the state of the controlled object and its derivative. Further, z3 is an estimated value of the action due to any uncertain model and uncertain disturbance.

The non-linear ordinary differential equation of the equation (12) can be calculated as the equation (14) by the approximate solution method by the Euler method shown in the following equation (13).

[0057]

[Equation 13]

[0058]

[Equation 14]

In Expression 14, t is a discrete time and h is a step width of discrete time. In this way, the adaptive gains β01, β02, β03, and the nonlinear functions g1, g2, g3
After determining, the state estimate displacement z1 is calculated at each discrete time t.
error ε (t) calculated as the difference between (t) and control target output y (t), state estimate displacement z1 (t), state estimate displacement derivative z2 (t), and uncertainty estimation Input z obtained by multiplying the value z3 (t) and the operation input to the controlled object by a known gain
A known action amount f0 (z1 is calculated based on u (t), z1 (t), z2 (t), and a known disturbance action amount w0 (t).
(t), z2 (t), w0 (t)) and the next discrete time t +
State estimated value displacement z1 and state estimated value displacement derivative z2 at h
, And the uncertainty estimation value z3 can be calculated. As described above, f0 (z1 (t), z2 (t), w0 (t)) may be ignored if the known amount of action is unknown.

In equation 14, the non-linear functions g1 (ε), g2
Selection of (ε) and g3 (ε) (hereinafter, “(t)” is abbreviated and expressed) is an important factor in determining the performance of the ESO 103. In the past literature, the inventor of the present application has adopted a non-linear function as shown in the following Expression 15.

[0061]

[Equation 15]

Here, sign (ε) is a function for calculating the code value (+1 or −1) of the error ε. However, this algorithm is relatively complicated, resulting in an increase in the amount of calculation and eventually in control performance. Therefore, in the present invention, the nonlinear functions g ₁ (ε), g ₂ (ε), and g
We invented an algorithm that realizes ₃ (ε) by a simple polygonal line function. This polyline function is the input to the function x
(Corresponding to ε described above) is expressed as a function of the following Expression 16 and FIG. 6 (a) or Expression 17 and FIG. 6 (b).

[0063]

[Equation 16]

[0064]

[Equation 17]

These polygonal line function algorithms are relatively simple, and only by selecting appropriate parameters d1, d2, k1 and k2, the ESO 103 can perform estimation with a small amount of calculation and good performance. As described above, the non-linear functions g1 (ε), g2 (ε),
And g3 (ε) are calculated as fpl2
(X, d1, k1) or fpl3 (x, d1)
, D2, k1, k2), the state estimation value displacement z1, the state estimation value displacement derivative z2, and the uncertain effect estimation value z3 can be calculated with a small amount of calculation.

The user associates each of g1 (ε), g2 (ε), and g3 (ε) with fpl2 (x, d1, k1) or fpl3 (x, d1, d2, k1, k2). Is performed by the non-linear function selection unit 114 in FIG. <O. S. E. Operational Principle of F 109> As a control target, as in the case of considering the ESO 103, consider a 1-input / output quadratic nonlinear system shown in Formula 7.

As described above, as ESO 103,
Since it has been shown that an observer can be designed to estimate the unknown dynamic characteristic f1 (.) Of the equation, S. E. F 1
In 09, by feeding back the estimated value to the manipulated variable u (FIG. 1) of the controlled object, the nonlinear characteristic f1 (.)
To compensate.

Now, the manipulated variable u (or u (t)) is decomposed into two.

[0069]

[Equation 18]

Here, if the uncertain effects such as the uncertain model and uncertain disturbance and the known effects such as the known model and known disturbance are called "disturbance effect" in a broad sense, the manipulated variable u
00 (or u00 (t)) is a term for feeding back a pure error of the controlled object that is not caused by the disturbance action. Hereinafter, this operation amount u00 is referred to as an error feedback operation amount. On the contrary, the manipulated variable u1 (or u1 (t)) is a term for compensating the disturbance action. Hereinafter, this operation amount u1 is referred to as a disturbance compensation operation amount.

Assuming that the disturbance compensation operation amount u1 can accurately compensate for uncertain effects such as uncertain models and uncertain disturbances and known effects such as known models and known disturbances, the first part on the right side of the equation (7)
It becomes possible to cancel the terms and the second term, and as a result,
The controlled system becomes almost the same as the system shown by the following equation, and the automatic disturbance rejection function is realized.

[0072]

[Formula 19]

As described above, ESO 1
The estimated value z3 (t) output by 03 indicates the estimated value of the action due to any uncertain model and uncertain disturbance. Also, the estimated state value displacement z1 (t) output by the ESO 103
And state estimated value displacement derivative z2 (t) and known disturbance action amount w0
Based on (t), the known action quantity f0 (z1 (t), z2 (t),
w0 (t)) can be calculated. Therefore, by calculating the disturbance compensation operation amount u1 (t) by the following formula 20, it is possible to accurately compensate the uncertain effects such as the uncertain model and uncertain disturbance and the known effects such as the known model and known disturbance. This makes it possible to bring the system to be controlled into the state shown by the equation (19) and realize the automatic disturbance elimination function.

[0074]

[Equation 20]

In the embodiment of the invention shown in FIG.
First, the known effect amount computing unit 105 outputs the estimated state value displacement z1 (t) and estimated state value displacement derivative z2 output by the ESO 103
(t) and the known disturbance action amount w0 (t), the known action amount f0 (z1 (t), z2 (t), w0 (t)) is calculated, and the adder 110 then calculates the calculated value. And the uncertain effect estimated value z3 (t) output from the ESO 103 are added, and the multiplier 1
11 multiplies the addition result by −1 / b to calculate the disturbance compensation operation amount u1 (t) shown in the equation (20).

In the conventional PID control, the disturbance compensation operation amount u
Instead of 1, the differential signal and the integral signal are generated directly from the target value v0 and the output error ε of the controlled object, and the manipulated variable u is generated in the form of their “combination” shown in the following equation.

[0077]

[Equation 21]

Compared with such a method, the method of the present invention is far superior in that it has a function of compensating for unknown disturbance. On the other hand, the error feedback manipulated variable u00 is a term for compensating the pure displacement of the controlled object which is not caused by the disturbance action. As mentioned above, ESO 103
The estimated values z1 (t) and z2 (t) output by the above equation indicate the displacement and the derivative of the estimated value of the state of the controlled object. In addition, A.
T. The v1 (t) and v2 (t) output by P 102 represent the displacement and displacement derivative of the transient process having the target value v0. Therefore, by calculating the errors ε 1 (t) and ε 2 (t) between the transient process of the target value and the state estimation value for each of the displacement and the displacement derivative, using these error amounts, The error feedback manipulated variable u00 (t) can be calculated.

[0079]

[Equation 22]

The inventor of the present application calculates a suitable nonlinear algorithm g (ε1 (t) as a method for calculating the error feedback manipulated variable u00 (t) based on the displacement error ε1 (t) and the displacement differential error ε2 (t). ), Ε 2 (t)) was invented. That is, the error feedback control input u00 (t) can be calculated based on the following equation 23.

[0081]

[Equation 23]

The inventor of the present application calculated the error feedback manipulated variable u00 based on the non-linear function calculation shown in the following formula 24 in the "automatic disturbance rejection controller (ADRC)" previously invented (discrete time The index “(t)” is omitted).

[0083]

[Equation 24]

Although this formula can accelerate the target following effect, it is not optimal as a combination of errors. Over the long term, many people have been studying what method can be used to reach the control target in an optimal manner in a certain sense. Then, from the pure integrator continuous type object, the ideal combination formula of the error shown by the following formula was obtained.

[0085]

[Equation 25]

However, this expression is an arithmetic expression that outputs only the values of + r and -r, and if this formula is used for direct control, the error feedback manipulated variable u ₀₀ cannot stop at the target value, and A high frequency of vibration is likely to occur near the value. FIG. 7 (a) is based on the equation 25 so that each value of the displacement error ε ₁ and the displacement differential error ε ₂ becomes 0 (that is, the error feedback manipulated variable u ₀₀ matches the target value). The change in the values of ε ₁ and ε ₂ when the compensation operation is performed by the following. As can be seen from this graph, the values of ε ₁ and ε ₂ oscillate near the origin.
Therefore, the non-linear function of the equation 25 has a problem that it is considerably difficult to use in the actual control process. Even with a simple modification, the effect was not very good, so it was difficult to spread this theory.

In order to solve the calculation stability problem of the tracking differentiator, the inventor of the present application, in the Chinese document [2] of Table 1 described above, at the sampling step h shown by the following formula 26, The synthesis function of time-opt is a discrete-time system that operates.
imal control of the discrete system with the sampl
ing step h.).

[0088]

[Equation 26]

As it is, this formula cannot be directly applied to the calculation of the error feedback manipulated variable u00. However, it has been found that this formula may be improved as shown in the following Expression 27 (hereinafter, the discrete time index “(t)” is considered).

[0090]

[Equation 27]

Here, r is a parameter. O. of FIG. S. E. F 109 executes the error feedback operation by executing the calculation of the above equation 27 based on the displacement error ε1 (t) and the displacement differential error ε2 (t) and the parameters r and h1 at every discrete time t. Output the quantity u00 (t).

In the equations (26) and (27), y has nothing to do with the output y of the controlled object in FIG. Also, a
Is not related to the acceleration a (t) in the equations 2 to 6 or the function a (t) in the equation 9. Both are variables used only within these expressions. The displacement error ε is shown in Fig. 7 (b).
Ε when the compensating operation is executed based on the equation (27) so that each value of ₁ (t) and displacement differential error ε ₂ (t) becomes 0.
The changes in the values of ₁ (t) and ε ₂ (t) are shown. Compared to Fig. 7 (a) based on Equation 25, the values of ε ₁ (t) and ε ₂ (t) do not oscillate at all near the origin, and a very excellent compensation operation is executed. You can see that

First, A. T. P 102 and ESO
The parameter h used by 103 is set in a variable register or the like not particularly shown (step 801 in FIG. 8).
The parameter h is a discrete time sampling step. Next, the maximum calculation time Tmax instructing where to stop the control is set in a variable register (not shown) or the like (step 802 in FIG. 8).

Next, A. T. The target value v0 used in the calculation by P 102 is set in a variable register or the like not shown (step 803 in FIG. 8). Next, A. T. P
The transient process time T used in the calculation by 102 is set in a variable register (not shown) or the like (step 804 in FIG. 8).

Next, the transient process pattern selection unit 113
At A. T. The function subroutine of the transient process pattern used by the P 102 for calculation is selected from a plurality of patterns stored in advance in a ROM (not shown) or the like based on a user instruction, and RA (not shown) is selected.
It is set to M or the like (step 805 in FIG. 8).

Next, each of the initial output values z1 (0), z2 (0), and z3 (0) of the ESO 103 at time t = 0 is reset to 0 (step 806 in FIG. 8). ). Next, the adaptive gain β01, which is used by the ESO 103 for calculation,
β02 and β03 are set in a variable register (not shown) or the like (step 807 in FIG. 8).

Next, in the non-linear function selection unit 114, ES
The function subroutines of the non-linear functions g1, g2, and g3 used by the O 103 for calculation are based on the user's instruction.
In particular, the function f stored in advance in a ROM (not shown) or the like
It is selected from either pl2 or fpl3 and is set in a RAM or the like (not shown). At the same time, the parameter set {d1, k1} (fpl2
Is selected) or {d1, d2, k1, k2}
(When fpl3 is selected) is also set in a variable register or the like not shown in the figure (the above is step 80 in FIG. 8).
8).

Next, the input gain coefficient b is set in a variable register or the like not particularly shown (step 80 in FIG. 8).
9). Next, a calculation subroutine of the function f0 for determining the known action amount is set in the RAM or the like not shown (step 810 in FIG. 8).

Next, the O. S. E. The parameters r and h1 used by the F 109 for calculation are set in a variable register or the like not shown (step 811 in FIG. 8). The value of the parameter h1 is set to be larger than the value of the sampling step h set in step 801.

Finally, O. S. E. The parameters d and d0 used by F 109 for the calculation are
It is calculated based on the parameter h1 set in step 801 and the parameter r set in step 811, and is set in a variable register (not shown) or the like (step 812 in FIG. 8). <Main Operation Flow> After the initial setting operation flow is executed, the main operation flow is started. FIG. 9 is a main operation flowchart. This operation flowchart is an operation in which the microprocessor that controls the overall operation of the optimum ADRC 101 in FIG. 1 executes a control program stored in a ROM (not shown) or the like while using a RAM (not shown) or the like as a work memory. Is realized as.

In the main operation flow, first, after the value of the time variable t assigned to a variable register (not shown) is reset to 0 (step 901 in FIG. 9),
The value of the time variable t is set in step 802 of FIG. 8 while the value of the time variable t is increased by the step width h set in step 801 of FIG. 8 at a predetermined discrete time interval (step 905 of FIG. 9). Until it is determined that the calculated maximum calculation time Tmax has been exceeded (the determination in step 906 in FIG. 9 is N
O)), at each discrete time t, A. T. P 102 operation processing (step 902 in FIG. 9), O.P. S. E. F 1
09 operation processing (step 903 in FIG. 9) and ESO
The operation process 103 (step 904 in FIG. 9) is sequentially executed.

When it is determined that the value of the time variable t exceeds the maximum operation time Tmax (the determination made in step 906 of FIG. 9 is Y).
When it becomes ES), the optimum ADRC control operation for one operation unit is completed. <A. T. Operation Flow of P102> FIG. 10 shows the A.P executed as the processing of step 902 of the main operation flow of FIG. T. It is an operation | movement flowchart which shows operation | movement of P102. This operation flowchart is based on T. P 1
The microprocessor assigned to the operation No. 02 of A.02 is stored in a ROM or the like (not shown). T. The P operation control program is realized as an operation to be executed while using a RAM (not shown) as a work memory.

First, as described above, the value of the time variable t is divided by the transient process time T set in step 804 of FIG. 8 to calculate the variable value τ (the value immediately before the equation 3). (See the description), and is held in a variable register (not shown) or the like (step 1001 in FIG. 10).

Next, using the function subroutine of the transient process pattern selected by the transient process pattern selection unit 113 in step 805 of FIG.
The transient process displacement v1 (t) and the transient process displacement derivative v2 (t) at the discrete time t are calculated by using any one of the formulas to the formula 6 and are stored in a variable register (not shown). Retained. At this time, the target value v0 set in step 803 of FIG. 8, the transient process time T set in step 804 of FIG.
The variable value τ calculated in step 1001 is used for the calculation (above, steps 1002 and 100 in FIG. 10).
3).

In this way, the A. T. P 102 is
At each discrete time t which is sequentially updated in the main operation flow of FIG. 9, the transient process displacement v1 with respect to the target value v0
(t) and the transient process displacement derivative v2 (t) can be generated. <O. S. E. Operation Flow of F 109> FIG. 11 shows the O.F.I. executed as the processing of step 903 of the main operation flow of FIG. S. E. It is an operation | movement flowchart which shows operation | movement of F109. This operation flowchart is based on the O.I.
S. E. The microprocessor assigned the operation of the F 109 is the O.F. S. E. The F operation control program is realized as an operation to be executed while using a RAM or the like (not shown) as a work memory.

First, based on the above-mentioned formula 22,
0, the transient process displacement v1 (t) at the discrete time t calculated in step 1002, and the state estimation at the discrete time t calculated one discrete time before (= t-1) in step 1206 of FIG. 12 described later. The displacement error ε1 (t) with respect to the value displacement z1 (t) and the transient process displacement derivative v2 (t) at the discrete time t calculated in step 1003 of FIG.
And the displacement error differential ε 2 (t) with the state estimation value displacement differential z 2 (t) at the discrete time t calculated one discrete time before (= t−1) in step 1207 of FIG.
Each is calculated and stored in a variable register or the like not shown (step 1101 in FIG. 11).

Next, according to the equation (27), the variable value y is calculated using the above ε1 (t) and ε2 (t) and the parameter h1 set in step 801 of FIG. Not held in a variable register or the like (step 1102 in FIG. 11). Next, the variable value y and the parameter r calculated in step 811 of FIG.
And the parameter d similarly calculated in step 812, the variable value a0 is calculated and held in a variable register (not shown) (step 110 in FIG. 11).
3).

Then, according to the equation 27, it is judged whether or not the value of the variable value y is less than or equal to the value of the parameter d0 calculated in step 812 of FIG. 8 (step 1 of FIG. 11).
104). If this determination is YES, the displacement error differential ε 2 (t) calculated in step 1101 and the step 801 in FIG. 8 are calculated based on the case 1 (upper side) of the calculation formula of the variable value a in the formula 27. The variable value a is calculated using the parameter h1 set in step 1 and the variable value y calculated in step 1102, and is stored in a variable register or the like not shown (above, step 1105 in FIG. 11).

On the other hand, if the determination in step 1104 is NO, the case 2 (lower side) of the calculation formula of the variable value a in the formula 27 is shown.
Based on the equation, the displacement error differential ε 2 (t) calculated in step 1101, the parameter d calculated in step 812 in FIG. 8, the variable value y calculated in step 1102, and the variable value y calculated in step 1103. The variable value a0 is calculated using the variable value a0, and is stored in a variable register or the like not shown (step 1106 in FIG. 11).

Subsequently, according to the equation 27, it is determined whether or not the value of the variable value a calculated in the above step 1105 or 1106 is less than or equal to the value of the parameter d calculated in step 812 of FIG. (Step 110 in FIG. 11
7). If this determination is YES, the variable value fst in the equation 27
Based on the case 1 (upper side) of the calculation formula of, the parameter r set in step 811 of FIG.
The function value fst is calculated using the variable value a calculated in 05 or 1106, and the value is held in a variable register (not shown) as the error feedback manipulated variable u00 (t) at the discrete time t ( Step 110 of FIG.
8).

On the other hand, if the determination in step 1107 is NO, the parameter r set in step 811 of FIG. 8 is calculated based on the case 2 (lower side) of the equation for calculating the variable value fst in the equation 27. , The function value fst is calculated using the variable value a calculated in step 1105 or 1106,
The value is held as an error feedback manipulated variable u00 (t) at the discrete time t in a variable register (not shown) or the like (step 1109 in FIG. 11).

Next, using the adder 110 and the multiplier 111, the disturbance compensation manipulated variable u1 (t) is calculated according to the equation (20). In this calculation, first, the state estimated value displacement z1 (t) at the discrete time t calculated one discrete time before (= t-1) in steps 1206 and 1207 of FIG. 12 described later.
And the state-estimated value displacement derivative z2 (t) and the known disturbance action amount w0 (t) at the discrete time t input from the outside, the known function calculation f0 (z1 By executing (t), z2 (t), w0 (t)), the known action amount f0 at the discrete time t is calculated and held in a variable register or the like (not shown). Next, the known action amount f0 at the discrete time t calculated as described above and step 12 of FIG.
In 08, the uncertain effect estimated value z3 (t) at the discrete time t calculated one discrete time before (= t-1) is added (adder 110), and (-1 / b) is added to the addition result. (The input gain coefficient b is set in step 809 of FIG. 8) is multiplied (multiplier 111), and the multiplication result is used as the disturbance compensation operation amount u1 (t) at the discrete time t, which is not shown in the variable register. Etc. (End of FIG. 11)
Step 1110).

Finally, the error feedback manipulated variable u00 (t) calculated in step 1108 or 1109 and the disturbance compensation manipulated variable u1 (t) are added (adder 112), and the manipulated variable u (t ) Is stored in a variable register (not shown) and is output to the control target (step 1111 in FIG. 11).

As described above, the O.V. S. E. F 10
9 can execute the optimal compensation operation for the controlled object. <Operation Flow of ESO 103> FIG. 12 is an operation flowchart showing the operation of the ESO 103 which is executed as the process of step 904 of the main operation flow of FIG. This operation flow chart shows an operation in which the microprocessor assigned with the operation of the ESO 103 executes the ESO operation control program stored in the ROM (not shown) or the like while using the RAM (not shown) or the like as the work memory. Will be realized.

First, the value of the manipulated variable u (t) at the discrete time t calculated in step 1111 of FIG. 11 is multiplied by the input gain coefficient b set in step 809 of FIG. The known action amount f0 at the discrete time t calculated in step 1110 of 11 is added to calculate the temporary variable value bu (t) + f0, which is held in a variable register (not shown) (step 1 in FIG. 12).
201).

Next, based on the equation (14), step 12
In 06, the state estimated value displacement z1 (t) at the discrete time t calculated one discrete time before (= t-1) and the controlled object output y (at the discrete time t (current) input from the controlled object t) is used to calculate the error ε (t) at the discrete time t (step 1202 in FIG. 12).

Next, based on the setting in step 808 of FIG. 8, expression 16 (when fpl2 is selected) or expression 1
According to equation 7 (when fpl3 is selected), the discrete time t
Non-linear function g1 (ε (t)) = fpl2 (ε (t)
, D1, k1) or g1 (ε (t)) = fpl3 (ε (t)
, D1, d2, k1, k2) are calculated (step 1203 in FIG. 12).

Similarly, based on the setting in step 808 of FIG. 8, the nonlinear function g2 (ε (t)) = fpl2 (ε (t), d1
, K1) or g2 (ε (t)) = fpl3 (ε (t), d1
, D2, k1, k2) are calculated (step 1204 in FIG. 12).

Further, based on the setting in step 808 of FIG. 8, the non-linear function g3 (ε (t)) = fpl2 (ε (t), d1,
k1) or g3 (ε (t)) = fpl3 (ε (t), d1, d
2, k1, k2) is calculated (step 120 in FIG. 12).
5).

Then, based on the equation (14), step 12
The estimated state value displacement z1 (t) and the estimated state value displacement derivative z2 (t) at the discrete time t calculated one discrete time before (= t-1) in 06 and 1207, and calculated in the above step 1203. Based on the nonlinear function g1 (ε (t)) at the discrete time t, the parameter h set at step 801 in FIG. 8, and the adaptive gain β01 set at step 807 in FIG. (= T
The state estimate displacement z1 (t + h) at + h) is estimated. This state estimated value displacement z1 (t + h) is replaced with the content of the variable value as z1 (t) at the next discrete time, and held in a variable register or the like not shown (step 1206 in FIG. 12). ).

Subsequently, based on the equation (14), step 120
7 and 1208, the state estimated value displacement derivative z2 (t) and the uncertain effect estimated value z3 (t) at the discrete time t calculated one discrete time before (= t−1) respectively, and in step 1204 described above. The calculated nonlinear function g2 (ε (t)) at the discrete time t, the parameter h set in step 801 of FIG. 8, the adaptive gain β02 set in step 807 of FIG. 8, and further in step 1201 Based on the calculated temporary variable value bu (t) + f0, the estimated state value displacement z2 (t + h) at the next discrete time (= t + h)
Is estimated. With respect to this state estimated value displacement z2 (t + h), the contents of the variable value are replaced as z2 (t) at the next discrete time, and are held in a variable register or the like not particularly shown (step of FIG. 12). 1207).

Finally, based on the equation (14), step 1
In 208, an uncertain effect estimated value z3 (t) at the discrete time t calculated one discrete time before (= t-1),
The nonlinear function g3 (ε (t)) at the discrete time t calculated in step 1205 and step 801 in FIG.
The estimated state displacement z3 (t + h) at the next discrete time (= t + h) is estimated based on the parameter h set in step 807 and the adaptive gain β03 set in step 807 in FIG. With respect to this state estimated value displacement z3 (t + h), the content of the variable value is replaced as z3 (t) at the next discrete time, and is stored in a variable register or the like not shown (step in FIG. 12). 1208).

As described above, the state estimation value displacement z1 (t), the state estimation value displacement derivative z2 (t), and the uncertain effect estimation value z3 (t) are calculated at each discrete time t with a small amount of calculation. can do. Description of Operation Example of Embodiment of the Present Invention The effects brought about by the embodiment of the present invention will be described below with reference to specific examples.

First, the controlled object is assumed as shown in the following expression 28.

[0125]

[Equation 28]

Here,

[0127]

[Equation 29]

Is an unknown disturbance. Operation target value ν 0 =
Set to 1. The transient process time T = 3 seconds. Further, as the pattern of the transient process, the one according to the above-mentioned equation 6 is selected. Furthermore, the nonlinear functions g1 (ε), g2
(Ε), g3 (ε) and the adaptive gains β01, β02, β03 are set as in the following equation.

[0129]

[Equation 30]

The manipulated variable u00 is calculated by the following equation. Discrete time step width h = 0.01.

[0131]

[Equation 31]

Experimental results obtained when the control is performed under the above set conditions are shown in FIG. 13 (when γ = 1) and FIG. 14 (γ).
= 10). In the case of FIG. 13, it can be seen that the disturbance has been compensated almost perfectly, and that it is following well even in the case of a large disturbance as shown in FIG.

It can be said that the above experimental results suggest that the "optimal automatic disturbance rejection controller" according to the present invention can control a very wide range of controlled object models. Description of Other Embodiments One embodiment of the present invention has been described in detail above. T. P 102, ESO
103, and O. S. E. Even each F 109 alone can exert an effect in combination with other control elements.

Regarding the ESO 103, the second-order nonlinear system is assumed as the controlled system in the description of the equations (7), (12), (14), etc. in the embodiment of the present invention. Is not limited to
Extension to the nth order is easy. Since the n-th order general system is disclosed as the equation (5) of the document B, for example, the nonlinear function gj (z1 (t) -x (t)) is shown in the embodiment of the present invention. There is no limitation in applying the equations (16) and (17).

In the present invention, it is possible to include an appropriate linear function as a substitute for the various nonlinear functions shown in the above-mentioned embodiments of the present invention.

[0136]

According to the present invention, it is possible to automatically observe the effects of the "internal disturbance (model)" and "external disturbance" of the controlled object, and to perform compensation. Therefore, it is possible to realize control with considerably high accuracy even in a complicated environment.

Further, since the non-linear algorithm for implementing the present invention is simple, an optimum automatic disturbance rejection control system can be easily designed, and the adaptive range of parameters is considerably wide, so that an ideal practical digital controller can be obtained. Can be realized. The features of the "optimum automatic disturbance rejection controller" realized by the present invention can be summarized as follows. 1) A non-linear fixed structure independent of the controlled object model. 2) Control can be performed quickly and without overrun or static error. 3) Since the physical significance of the parameters is clear, it is easy to adjust the parameters. 4) Since the algorithm is simple, it is an ideal digital controller that can realize high-speed and highly accurate control. 5) It is not necessary to measure the disturbance, and the influence of the disturbance can be eliminated. 6) It is irrelevant to the linear, nonlinear, steady, and non-steady state of the model. 7) It is better if the controlled object model is known, but it does not matter if it is unknown. 8) A large time delay controlled model can be easily controlled. 9) Decoupling control is particularly simple.

Presently, the majority of industrial controllers have emerged in the form of digital controllers, and older analog controllers have also been replaced by digital controllers. The controller industry is entering an era of digitization, modularization and integration.
"Optimal automatic disturbance rejection controller" realized by the present invention
Is a product that meets the needs of this era. This controller can replace the PID controller used in the field of more efficient and highly accurate process control and various existing high-level controllers.

Further, according to the present invention, correspondence to various controlled object models (many controlled object models belong to the same type) can be easily realized only by adjusting the parameters in the initial setting. . The "Automatic Disturbance Rejection Controller (ADRC)" that is the basis of the present invention has already been used for high-speed and high-accuracy control of "robots", dynamic endurance machine group control, furnace temperature control, generator excitation control, magnetic suspension stroke control. , 4 cylinder coordinated control, transmission motion control, asynchronous machine frequency conversion speed control, high-speed and high-accuracy machining lathe control, etc.
The ideal control effect is obtained. In addition, in different industrial areas such as "electric power system controllable continuous compensation control", "electric power system stationary idling compensation control", "seismic resistant building system control", "spacecraft attitude control", "moving body platform control", etc. , The applied research has obtained ideal results and shows great applicability.

The new "optimal automatic disturbance rejection controller" (Optimal ADRC) realized by the present invention has a simpler algorithm and higher control efficiency than its predecessor "Automatic disturbance rejection controller (ADRC)". Therefore, its application range can be further expanded.

[Brief description of drawings]

FIG. 1 is a configuration diagram of an embodiment of the present invention.

FIG. 2 is a characteristic diagram of a transient process pattern 1.

FIG. 3 is a characteristic diagram of a transient process pattern 2.

FIG. 4 is a characteristic diagram of a transient process pattern 3.

FIG. 5 is a characteristic diagram of a transient process pattern 4.

FIG. 6 is a characteristic diagram of a polygonal line function for ESO.

FIG. 7: O. S. E. It is a characteristic view of the optimal nonlinear function for F.

FIG. 8 is a flowchart of an initial setting operation.

FIG. 9 is a main operation flowchart.

10: A. T. It is a P operation | movement flowchart.

FIG. S. E. 9 is an operation flowchart of F.

FIG. 12 is an operation flowchart of ESO.

FIG. 13 is a characteristic diagram of experimental results (γ = 1).

FIG. 14 is a characteristic diagram of experimental results (γ = 10).

[Explanation of symbols]

101 Optimal ADRC (Optimal Automatic Disturbance Rejection Controller) 102 A. T. P (transient process setter) 103 ESO (extended state observer) 104, 111 multiplier 105 known action amount calculators 108, 110, 112 adder 107 error calculator 108 differential error calculator 109 O. S. E. F (optimum state error feedback device) 113 Transient process pattern selection unit 114 Non-linear function selection unit

Continued Front Page (72) Inventor Han Jing Qing, People's Republic of China, Beijing, Haidian District, Zhongguancun 935, No. 610 (56) References JP-A-7-56634 (JP, A) JP-A-5-265514 (JP, A) JP 5-143106 (JP, A) JP 60-156117 (JP, A) JP 9-242507 (JP, A) JP 2001-325006 (JP, A) FENG G, HUANG L , ZH U D (Tsinghua Uni v., Beijing, CHN), A Nonlinear Auto-Disturbance Rejection Controller for Induction Motor. , Proceedings. IECON (1998 IEEE 24TH ANNNUAL CONFERENCE OF THE IEE INDUSTRIAL ELE CRONICS), USA, January 18, 1999, VOL. 1998, NO. VOL. 3, p. 1509-1514 Bags Mahawan, Luo Sunghua, Han Kyo Kiyo, Shinichi Nakajima, High-speed and high-precision motion control of robots by extended state observer, Journal of the Robotics Society of Japan, Japan, March 15, 2000, VOL. 18, NO. 2, p. 244-251 (58) Fields investigated (Int. Cl. ⁷ , DB name) G05B 11/36-13/02

Claims (2)

(57) [Claims] 1. An operation for converting an error between a displacement of an estimated value of a controlled object state and an actual displacement amount of the controlled object state using a conversion function capable of including a non-linear function,
An extended state observation method using an observer capable of observing an uncertain effect including an unknown disturbance and an unknown dynamic characteristic of a controlled system via a state variable, which is an operation for converting the error using a conversion function. Is a polygonal line function fp expressed by the following equation that approximates the error to the conversion function.
l ₂ (x, d ₁ , k ₁ ) or fpl ₃ (x, d ₁ , d ₂ ,
k ₁ , k ₂ ) is executed as an operation equivalent to an operation using any one of them, and the estimated value of each dimension of the state of the controlled object and the estimated value of the uncertain effect are calculated based on the output value of the operation. Is calculated by using the observer. An extended state observation method comprising: [Equation 1] Here, x: input to the function, sign (x): function for calculating the code value (+1 or -1) of the input x, d _{1 ,} d _{2 ,}
k _{1 ,} k ₂ : variable parameters 2. A displacement error, which is an error between the displacement of the estimated value of the controlled object state and the displacement of the transient process of the target value, the derivative of the displacement of the estimated value of the controlled object state, and the transient process of the target value. And a displacement differential error which is an error with respect to the differential of the displacement, and calculates a conversion function that can include a non-linear function that inputs the displacement error and the displacement differential error and converges both of these errors to zero, A feedback control method for compensating for a displacement of a state of the controlled object by calculating an error feedback manipulated variable which is an operated amount for a controlled object, and compensating for a displacement of a state of the controlled object, wherein the calculation by the conversion function is performed by When the error and displacement differential error are converged to zero, it has the characteristic of suppressing the vibration of those error values near zero, and is equivalent to the operation shown by the following equation. Feedback control method characterized by comprising rows, the process. [Equation 2] Here, t: discrete time, ε ₁ (t): input of displacement error at discrete time t, ε ₂ (t): input of differential displacement error at discrete time t, r: set in relation to acceleration of transient process Parameters, h ₁ : constant parameter, y: internal variable, a ₀ : internal variable, sign (y) and sign
(A): a function that calculates the sign value (+1 or -1) of the input y or a, a: internal variable, fst (ε ₁ (t), ε ₂ (t),
r, h): nonlinear function value, u ₀₀ (t): error feedback manipulated variable at discrete time t